The embodiments described in this section could be pursued but are not necessarily embodiments that have previously been conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the embodiments described in this section qualify as prior art merely by virtue of their inclusion in this section.
An abacus is known as a mechanical computing device, which is used to perform basic numerical calculation of addition, subtraction, multiplication, and division. Different types of abacuses have been used for calculations for many centuries. Despite development in electronic calculators and computers, some abacuses (for example, the Japanese soroban), are still in wide use in some countries. Abacuses can be also used as a tool for teaching and developing calculation skills in children and adults, especially mental calculation skills. Students can be first taught to use an abacus to perform arithmetical calculations. Then the students can be trained to imagine the abacus and mentally manipulate images of the abacus to perform the arithmetical calculations.
Some existing systems for teaching calculation skills using an abacus include electric or electronic abacuses connected to a computer for checking the results of calculations. Other known systems for training include online applications that may simulate calculations using an abacus.
The existing abacus based training systems have some disadvantages related to solving a mathematical problem with multiple operations. One of the disadvantages is the difficulty of determining the exact operation or step at which a mistake is made while performing multiple operations. Another disadvantage, entailed by the first one, is that when the student makes a mistake in at least one of the multiple operations of low level complexity, he/she may arrive at an operation that requires knowledge of an operation of a high level of complexity. Yet another disadvantage is that the existing training systems are not suitable to be used in group training because they do not allow to provide mathematical problems to the students with different skills.